Question: A circle has a sector with area $\dfrac{56}{5}\pi$ and central angle $112^\circ$. What is the area of the circle? ${36\pi}$ $\color{#9D38BD}{112^\circ}$ ${\dfrac{56}{5}\pi}$
The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{112^\circ}{360^\circ} = \dfrac{56}{5}\pi \div A_c$ $\dfrac{14}{45} = \dfrac{56}{5}\pi \div A_c$ $A_c \times \dfrac{14}{45} = \dfrac{56}{5}\pi$ $A_c = \dfrac{56}{5}\pi \times \dfrac{45}{14}$ $A_c = 36\pi$